Espacio-tiempo caótico

Abstract

In this paper we have shown how the consideration of a chaotic mechanics supplies a redefinition of special-relativistic space-time. In particular chaotic time means no possibility of defining temporal ordering and implies a breakdown of causality. The new chaotic transformations among 'undetermined' space-time coordinates are no more linear and homogeneous. The principles of inertia and of energy-impulse conservation are no longer well defined and in any case no more invariant.

Keywords

Chaos

non-linear dynamics

relativity

space-time

References

Agodi, Attilio and Anthony Cassarino. “Time ordering and the Lorentz group”. Foundations of Physics. Feb. 1982: 137-152. Print.

Anderson, Philip W., Arrow, Kenneth and David Pines. Eds. The Economy as Evolving Complex System. New York: Wesley Publishing Company, 1988. Print.

Arecchi, F. Tito, Basti, Gianfranco, Boccaletti, Stefano and Alessio Perrone. “Adaptive recognition of a chaotic dynamics”. Europhysics Letters. 1994: 327-332. Print.

Bai‑lin, Hao. Chaos, No. 1. Singapore: World Scientific, 1984. Print.

Barrow, John D. “Chaotic behaviour in general relativity”. Physics Reports. May. 1982: 1-49. Print.

---. “General relativistic chaos and nonlinear dynamics”. General Relativity and Gravitation. Jun. 1982: 523-524. Print.

Barut, Asim O. Geometry and Physics: Non-Newtonian Forms of Dynamics. New York: Humanities Press International, 1990. Print.

Born, Max, Hooton, D.J. and Nevill F. Mott. “Statistical dynamics of multiply-periodic systems”. Mathematical Proceedings of the Cambridge Philosophical Society. Apr. 1956: 287-300. Print.

Chernikov, AA., Tél, T., Vattay, G. and G. M. Zaslavsky. “Chaos in the relativistic generalization of the standard map”. Phys. Rev. Oct. 1989: 4072. Print.

da Costa, Newton and Franciso Antonio Doria. “Undecidability and incompleteness in classical mechanics”. Internat. J. Theoret. Phys. 1991: 1041-1073. Print.

Di Prisco, Alicia, Herrera, Luis and Jaume Carot. “On the chaotic behaviour induced by surface phenomena in some general relativistic stellar models”. Physics Letters A. May. 1990: 105-109. Print.

Dilts, Gary. “Chaotic plane-wave solutions for the relativistic selfinteracting quantum electron”. Physica D: Nonlinear Phenomena. Dec. 1986: 470-478. Print.

Earman, John. A Primer on Determinism. Dordrecht: Springer, 1986. Print.

Eckmann, Jean-Pierre and David Ruelle. “Addendum: Ergodic theory of chaos and strange attractors”. Rev. Mod. Phys. Oct. 1985: 1115. Print.

Einstein, Albert. “Zur Elektrodynamik bewegter Körper”. Annalen der Physik. 1905: 891-921. Print.

Eddington, Arthur S. The Mathematical theory of relativity. Cambridge: Cambridge University Press, 1923. Print.

---. The Nature of the Physical World. Michigan: MacMillan, 1928. Print.

Finkelstein, David. “Matter, space and logic”. Boston Studies in the Philosophy of Science. 1968: 199-215. Print.

Giannetto, Enrico. “Henri Poincaré and the rise of special relativity”. Hadronic Journal. 1995 (Sup.): 365-433. Print.

---. “Max Born and the Rise of Chaos Physics”. Atti del XIII Congresso Nazionale di Storia della Fisica. Ed. Andrea Rossi. Lecce: Conte, 1995. Print.

Havas, Peter. “Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity”. Reviews of Modern Physics. Oct. 1964: 938. Print.

Il‑Tong, Cheon. “Extended Theory of Special Relativity and Photon Mass”. Lettere al Nuovo Cimento. Dic. 1980: 518-520. Print.

Klein, Felix. “Vergleichende Betrachtungen über neuere geometrische Forschungen”. Math. Ann. 1893: 63-100. Print.

Lorenz, Edward. “Deterministic Nonperiodic Flow”. Journal of the Atmospheric. 1963: 130-141. Print.

Moore, Cristopher. “Unpredictability and undecidability in dynamical systems”. Phys. Rev. Lett. May. 1990: 2354. Print.

Poincaré, Henri. Les méthodes nouvelles de la mécanique céleste. Paris: Gauthier Villars, 1899. Print.

---. “L’état actuel et l’avenir de la physique mathématique”. Bulletin des Sciences Mathématiques. 1904: 302-324. Print.

---. “Sur la dynamique de l’électron”. Comptes Rendus de l’Académie des Sciences. 1905: 1504-1508. Print.

---. “On the dynamics of the electron: Introduction”. Rendiconti del Circolo Matematico di Palermo. 1906: 129-145. Print.

Prigogine, Ilya. La nascita del tempo. Napoli: Theoria, 1988. Print.

---. Le leggi del caos. Bari: Laterza, 1993. Print.

Rasband, S. Neil. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, 1990. Print.

Ruelle, David. Elements of differentiable dynamics and bifurcation theory. New York: Academic Press, 1989. Print.

Schroeder, Manfred. Fractals, Chaos, Power Laws: Minutes from an infinite paradise. London: Dover Publications, 2009. Print.

Segal, Ezra. Mathematical Cosmology and Extragalactic Astronomy. New York: Accademic Press, 1976. Print.

Svozil, Karl. “Quantum field theory on fractal spacetime: A new regularisation method”. Journal of Physics A: Mathematical and General. 1987: 3961. Print.

Svozil, Karl and Anton Zeilinger. Dimension of Space-Time. Vienna: Institut für Theoretische Physik, 1985. Print.

Tyapkin, Alexey. “Expression of the General Properties of Physical Processes in the Space-Time Metric of the Special Theory of Relativity”. Soviet Physics Uspekhi. 1972: 205-225. Print.

Whitehead, Alfred North. Space, Time and Relativity. Proceedings of the Aristotelian Society. 1915-1916: 104-129. Print.

Zak, Michail. “Introduction to Terminal Dynamics”. International Journal of Theoretical Physics. 1993: 59-87. Print.

Zardecki, Andrew. “Modeling in chaotic relativity”. Phys. Rev. Sep. 1983: 1235. Print.

Zeeman, E.C. “Causality Implies the Lorentz Group”. J. Math. Phys. Apr. 1964: 490-493. Print.

Zeilinger, Anton and Karl Svozil. “Measuring the Dimension spacetime”. Phys Rev. Lett. Jun. 1985: 2553. Print.